#4741: [with rebased patch, needs work] Implement S-integral point finding for
elliptic curves over Q
---------------------------+------------------------------------------------
Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Resolution:
Keywords: |
---------------------------+------------------------------------------------
Changes (by was):
* summary: [with rebased patch, needs review (finally)] Implement
S-integral point finding for elliptic curves
over Q => [with rebased patch, needs work]
Implement S-integral point finding for elliptic
curves over Q
Comment:
REFEREE REPORT:
I broke it again with a simple for loop.
{{{
sage: EllipticCurve('2534g1').S_integral_points([13,2])
...
--> 576 return self[0]/self[2], self[1]/self[2]
577
578 def is_divisible_by(self, m):
/home/was/build/sage-3.2.2.alpha2/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:9074)()
/home/was/build/sage-3.2.2.alpha2/local/lib/python2.5/site-
packages/sage/rings/padics/padic_capped_relative_element.so in
sage.rings.padics.padic_capped_relative_element.pAdicCappedRelativeElement._div_
(sage/rings/padics/padic_capped_relative_element.c:11055)()
ZeroDivisionError: cannot divide by zero
}}}
This is the loop that got it:
{{{
sage: for E in cremona_optimal_curves([1000..10000]):
if E.rank() == 2:
print E.cremona_label(),
E.S_integral_points([13]+[E.conductor().factor()[0][0]])
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4741#comment:23>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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